I would add that technically there’s not really any combinations. I would say that their sounds are categorized based off of combinations of consonant and vowel sounds, but really there’s just a single set number of sounds. 15 consonant sounds and 5 vowel sounds could make WAY more combinations than what’s actually available in Japanese. Also, consonant-vowel combination isn’t one to one. Not being nitpicky, I just wanted to add that little bit of info.
You’ll get different counts based on the method of counting syllables, but I’ve read that English has 7,931 syllables while Japanese has only 416. (from https://news.ycombinator.com/item?id=2976547 Their source was a journal article that I can’t easily get access to)
(On to the main topic:)
Yes there are a ton of homophones and specifically because of this. Relating to what Leebo
said; Make sure, though, that you’re not mistaking the readings of kanji for actual words you can use. Some of them can, but I’m slightly sure that a majority of them can’t.
Now the reason that are a ton of kanji with こう as a pronunciation is because of how those sounds were imported from China a long time ago. The original Chinese sounds that they come from are actually mostly distinct from each other, but they had to be simplified in order to become compatible with Japanese’s much simpler phonetic system. This happened to many different kanji.
By the way, (if you didn’t already know) these readings of Chinese origin are called the On’yomi (音読み) of a kanji while the Japanese reading is the kun’yomi (訓読み) and it’s pretty important to internalize what those are. But basically on’yomi are usually only used in kanji compounds while kun’yomi will be single words that will likely include attached hiragana. (Usually, not always.)
My own related question, now: Is there a name for Kanji that share on’yomi readings?